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Research Papers

# Continuum Mechanics Analysis of Fracture Progression in the Vitrified Cryoprotective Agent DP6

[+] Author and Article Information
Paul S. Steif, Matthew C. Palastro

Biothermal Technology Laboratory, Department of Mechanical Engineering,  Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15237

Yoed Rabin1

Biothermal Technology Laboratory, Department of Mechanical Engineering,  Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15237rabin@cmu.edu

1

Corresponding author.

J Biomech Eng 130(2), 021006 (Mar 28, 2008) (7 pages) doi:10.1115/1.2898716 History: Received February 20, 2006; Revised August 03, 2007; Published March 28, 2008

## Abstract

As part of an ongoing effort to study the continuum mechanics effects associated with cryopreservation, the current report focuses on the prediction of fracture formation in cryoprotective agents. Fractures had been previously observed in $1ml$ samples of the cryoprotective agent cocktail DP6, contained in a standard $15ml$ glass vial, and subjected to various cooling rates. These experimental observations were obtained by means of a cryomacroscope, which has been recently presented by the current research team. High and low cooling rates were found to produce very distinct patterns of cracking. The current study seeks to explain the observed patterns on the basis of stresses predicted from finite element analysis, which relies on a simple viscoelastic constitutive model and on estimates of the critical stress for cracking. The current study demonstrates that the stress, which results in instantaneous fracture at low cooling rates, is consistent with the stress to initiate fracture at high cooling rate. This consistency supports the credibility of the proposed constitutive model and analysis, and the unified criterion for fracturing, that is, a critical stress threshold.

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## Figures

Figure 1

Schematic illustration of (a) the macroscope setup (6), (b) the thermal stress problem analyzed in the current study, and (c) a closer view of the bottom of the vial, including the location of the thermocouple junction

Figure 2

Cracking in the CPA DP6, recorded with a cryomacroscope (Fig. 1), subject to slow cooling rate when the temperature at the center of the vial is −127.2°C before (a) and after (b) cracking, and subject to a fast cooling rate when the temperature at the center of the vial is −129.8°C (c) and −156.4°C (d)

Figure 3

Best-fit results for the heat transfer coefficient by convection (350W∕m2K), for the fast cooling case. Temperature measurements are compared to simulation results at the geometric center of the CPA, using ANSYS and the thermophysical properties listed in Table 1. For reference, two additional cases are plotted using convection coefficient values of 250W∕m2K and 450W∕m2K.

Figure 4

Simulated temperature distribution in the CPA for the fast (left column) and slow (right column) cooling rates, at three representative temperatures, Tc, at the geometrical center of the CPA

Figure 5

Circumferential stress distribution in the CPA as predicted by ANSYS , for the cases of fast (left column) and slow (right column) cooling rates, at three representative temperatures, Tc, at the geometrical center of the CPA. These stress distributions correspond to the temperature distributions presented in Fig. 4.

Figure 6

Circumferential stress distribution along the top and bottom surfaces of the CPA when the center temperature Tc reaches values of (a) −120°C and (b) −130°C

Figure 7

Predicted (solid curve) and observed (data points) crack front locations in the CPA as a function of centerline temperature Tc for the case of fast cooling. Predicted location is based on FEA and corresponds to a tensile stress level of 1.8MPa.

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